Your EULA does not permit what you have planned. You are entitled to use the original distribution of XP that came with your machine, and you have no license to another version of XP.
But I am less sanguine that member tf1 above that it would even work.
OEMs are given a choice by Microsoft of either a pure CD Key instllation or to BIOS lock the image to a unique identifier in the BIOS.
I do not know what version was used in your particular case. There is a further complication: the legitmacy of any key is determined by the PID on the CD itself.
First, find your setupp.ini file in the i386 directory on your Windows XP CD. Open it up, it'll look something like this:
ExtraData=707A667567736F696F697911AE7E05
Pid=55034000
The Pid value is what we're in this for. What's there now looks like a standard default, but that is no good. There are special numbers that determine if it's a retail, OEM, volume license or other edition. First, we must break down that number into two parts. The first five digits determines how the CD will behave, i.e. is it a retail CD that lets you clean install or upgrade, or an OEM CD that only lets you perform a clean install? The last three digits determine what CD key it will accept.
Here are the individual values, the first and last values are the important ones to determine if any key will fit:
[tt]
Type Type ID Key ID
Retail = 51882 335
Volume License = 51883 270
OEM = 82503 OEM
(There are other PIDs)
Then there is BIOS locking. This is often used, and often used by Dell, to ensure that their distributed CD images are not used on anything other than a range of CD Keys and qualifying BIOS versions.
As a guess, what you have is a plain vanilla OEM release, and the Dell key will not work with another OEM distribution because of the PID.
Faced with breaking the EULA, and possibly losing everything in a working system to discover that you cannot install XP after all, just clean up the "crap." XP is not like Win9x where there is substantial benefit to regular clean installs. Clean up, defragment and away you go safely.